Tidal effects on primordial black hole capture in neutron stars

We revisit the problem of the capture of a primordial black hole (PBH) by a neutron star, accounting for the tidal perturbation from a nearby star or planet. For asteroid-mass PBHs, which could constitute all of the dark matter in the universe, a weakly bound post-capture orbit could be tidally disturbed to the point of preventing the PBH from settling in the neutron star and consuming it within a cosmologically short timescale. We show how this effect depends on environmental parameters and can weaken the proposed constraints based on observations of old neutron stars in high-density dark matter environments for PBH masses $\lesssim 10^{22}\,$g. We also provide approximate analytical formulae for the capture rates.